Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror Symmetry

Physics – High Energy Physics – High Energy Physics - Theory

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12 pages, LaTeX (Replaced version corrects an error in the formula for bundle $B'$ on page 5, and changes the order of some en

Scientific paper

Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy certain incidence properties are calculated, and shown to agree with the numbers predicted by Greene, Morrison, and Plesser using mirror symmetry in every instance. This increases the number of verified predictions from 3 to 65. Calculations are performed using the Maple package {\sc schubert} written by Katz and Str{\o}mme.

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